With the November midterm elections still more than two months away, outside groups have already spent more than $155 million to influence federal elections. But while most of that money has gone toward electing candidates based on their party affiliation or ideology, a few groups have been spending with a very different goal: changing the way elections are funded.

A 2012 poll found nearly 7 in 10 Americans would prefer that super PACs — political committees that can raise and spend unlimited sums of money for or against federal candidates — were banned entirely. But with a Supreme Court majority that believes political spending is protected free speech and a Republican Party largely united against even the most limited reforms, big money continues to exert out-sized influence in Washington, DC.

The most visible of the superPACs working to eliminate superPACs and get big money out of politics, Larry Lessig’s Mayday PAC, has raised more than $7.8 million in just a few months of its existence. It aims to make a splash in a few races this year, massively reshape Congress in the 2016 elections, and get legislation enacted to reduce the influence of money in elections in early 2017.

But how can it — or others with similar aims but different approaches — succeed at fixing the system, by working within the system?

In an interview, Lessig told ThinkProgress that to change the system, Mayday must demonstrate to the “political people in Washington that Americans care about” getting big money out of elections and “are willing to vote on the basis of it.” To do this, his super PAC will endorse eight candidates this year and work to show that it can “move the dial enough to make progress” in those races.

The group’s plan originally called for it to play in five “pilot intervention” races this year, but due to better-than-expected fundraising — through small donors and through matching contributions from wealthy high-tech investors like Sean Parker (former president of Facebook and co-founder of Napster), Peter Thiel (co-founder of PayPal and Palantir Technologies), and Reid Hoffman (co-founder of LinkedIn) — it has expanded to eight. To date, Mayday has announced five of its eight 2014 endorsements.

The aim of these interventions is to support candidates who back reform against those who do not. The sort of reforms Mayday and its endorsed candidates back would create some sort of public financing for Congressional candidates who rely on small-dollar donations. This would be accomplished by providing matching funds to candidates, by providing vouchers or tax credits to citizens who want to contribute to candidates, or some combination thereof. Several states and localities have implemented similar systems, but efforts to do the same for Congressional elections have so far gone nowhere.

Lessig explained that the selected races “can’t be too easy — we could pick 8 races with Democrats who already support reform and no one would believe [we’d made a difference] because they’re gonna win anyway,” but also “can’t be too difficult, because we’ve got to show we can move the dial enough to actually make progress, eventually get enough seats to get a Congress committed to reform.” The endorsements also were designed to include both Democrats and Republicans, based on the group’s belief that “even though Democrats have taken the lead, we’ll never get fundamental reform unless its something Democrats and Republicans will sign onto,” he noted.

The initial five are something of an odd mix. The group backed longshot New Hampshire Senate candidate Jim Rubens in the upcoming Republican primary (though not for the general election, where he’d face a pro-reform incumbent in Sen. Jeanne Shaheen (D)), the reelection of Congressman Walter Jones (R-NC) and Congresswoman Carol Shea-Porter (D-NH), and two Democrats seeking open House seats: Ruben Gallego in Arizona’s 7th Congressional District and Staci Appel in Iowa’s 3rd.

But, he said that in close districts like Iowa’s 3rd and New Hampshire’s 1st, he is hopeful that Mayday’s efforts could make a quantifiable difference, injecting the issue of money in politics into the race so that “it resonates” with voters and helping the pro-reform endorsed candidates win. The three other races, he promised, would include challengers to entrenched incumbents, making impact much easier to quantify.

“To us, we’ll be looking for how we moved the dial between before our intervention and after and whether we can show through the data that a significant proportion of that movement was because of us. We’re creating the conditions to make that possible, by having the right kind of data collected, the right kind of ongoing process to do that,” Lessig observed. The challenge, he notes, is “to win enough to make people think ‘I didn’t think that was possible but it turns out it is.'” And if the group can do this, he believes it would not only create a roadmap for a larger effort in 2016 — it might also scare “a whole bunch” of other incumbents into discovering that they support reform too.

Darrell M. West, vice president and director of governance studies at the Brookings Institution, told ThinkProgress that this is “not impossible, but it certainly is very challenging.” “The biggest challenge in a campaign finance area is public cynicism: it’s hard to rally the public when they think everybody’s a crook and all politicians are beholden to special interests. That makes it difficult for them to believe it’s ever gonna be better.”

While Mayday has raised the most money of any such group, it is not the first effort to elect more reformers to Congress in hopes of sending a message to incumbents who defend the status quo. In 2012, a super PAC called Friends of Democracy raised and spent almost $2.5 million to elect pro-reform challengers to anti-reform incumbents. Seven of the eight candidates backed by the group against House incumbents were victorious.

David Donnelly, director of Friends of Democracy and president and CEO of the pro-reform Every Voice, told ThinkProgress that his group “pioneered this work of driving electoral consequences for being bad on the issue of money in politics” and “adoption of that strategy by others is welcome and an indication that what we’ve done has worked.” He noted that the two groups are working “side by side” toward the same general goal.

But even though Every Voice demonstrated success in 2012 — Donnelly said that “in six of the seven races in which our candidate won, the number of voters we targeted in a persuasion mailing was larger than the margin of victory” and that “polling after the race showed corruption and money in politics” ranked ahead of even the economy and jobs as an issue of concern for those voters — few in the Republican House have taken up the cause of reform. Indeed earlier this year, Congress dismantled one of the few remaining pieces of an already broken public financing system for presidential candidates and party conventions. “I think that has a huge amount to do with what [Senate Minority Leader] Mitch McConnell thinks.” McConnell has made opposition to campaign finance reform a “pet cause” and has exerted “outsized” influence, in both the Senate and House, Donnelly observed. The group hopes that if McConnell loses this November, more Republicans will join the effort.

A pair of other groups have taken a different approach toward trying to reform the money in politics system. CounterPAC has worked to reduce the influence of super PACs by pushing candidates to enter into a “people’s pledge” to dissuade outside spending. WolfPAC is pushing to elect state legislators who will back an Article V constitutional convention to circumvent Congress and amend the constitution to include a “Free and Fair Elections” provision.

Lessig said the groups “all aim at the same ends, but are following different paths. All paths should be followed.” In the end, he explained, reformers need a “Roger Bannister moment” for political insider circles. “Insiders say impossible to win on the basis of this issue, like they said it was impossible to run a mile in less than 4 minutes). We want to demonstrate that you can.”

West of Brookings notes that so far, these efforts have not worked. “Historically, successful social movements on money in politics have required a really big scandal that galvanized public attention and allowed groups to claim we need systemic change — the Progressive Era and Watergate period have been the two major reform period.” But, he notes, the current system of “large money and secrecy,” could be the “perfect recipe for a major scandal.”

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